The Wisconsin Badgers are not officially out of the bowl eligible race. Sure, six wins makes them a shoe-in for a bowl but there are plenty of five-win teams that get into bowls with the right circumstances. Wisconsin is actually on a track towards those circumstances but a ton would have to happen for them to be invited.
According to Erik Buchinger, a Forbes.com writer who knows all the ins and outs of how a five-win team can get into a bowl, Wisconsin still has insane odds to get invited. Wisconsin sports writer, Zach Heilprin, inquired of Buchinger and Buchinger responded that the "Badgers need to beat Minnesota and for Mississippi State, Kansas, Buffalo, Temple, North Carolina, Delaware, Army, Temple, Auburn, Kentucky, Florida State, Baylor, Kansas State, UCF, Washington State, Rice, Louisana, and Texas State to combine for a 3-15 record or worse next weekend."
Note: The author accidentally records Temple twice which means it's probably more like 2-15 or maybe 3-14.
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That's a lot of losses that Wisconsin would need to rely on, and this is all assuming that Luke Fickell would even accept a bowl invite if one were to come for a five-win team. Oh, and this is also assuming they can get the axe back. There's no such thing as a four-win bowl team.
The reason the list is so extensive is that a five-win team making a bowl all depends on how many six-win teams there are. If there are plenty of six-win teams, then there's no need to invite a five-win team. So Wisconsin needs a bunch of chaotic losses this weekend from these 18 teams. Three wins and 14 losses.
While this is all pretty crazy to think about, especially given that a few weeks ago this team seemed destined for a two-win season, now, there's a chance for five, and the vibes are up, and there's a strong chance that Wisconsin can bring home the axe this weekend.